What is the integral of 1/(xsqrt(ln(2x))) ?

The integral of 1/(xsqrt(ln(2x))) is 2sqrt(ln(2x))+C

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integral of 1/(xsqrt(ln(2x)))

\int \frac{1}{x ln ( 2 x )} d x

2 ln (2 x) + C

Solution steps

\int \frac{1}{x ln ( 2 x )} d x

Apply u-substitution

: \int \frac{1}{u ln ( u )} d u

= \int \frac{1}{u ln ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Apply the Power Rule

: 2 v^{\frac{1}{2}}

= 2 v^{\frac{1}{2}}

Substitute back

= 2 ln^{\frac{1}{2}} (2 x)

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 ln (2 x)

Add a constant to the solution

= 2 ln (2 x) + C

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What is the integral of 1/(xsqrt(ln(2x))) ?
The integral of 1/(xsqrt(ln(2x))) is 2sqrt(ln(2x))+C